3 Description

Because κ1A is infinite if A is singular, the routine actually returns an estimate of the reciprocal of κ1A.

The routine should be preceded by a call to F06RCF to compute A1 and a call to F07FDF (DPOTRF) to compute the Cholesky factorization of A. The routine then uses Higham's implementation of Hager's method (see Higham (1988)) to estimate A-11.

On entry: the first dimension of the array A as declared in the (sub)program from which F07FGF (DPOCON) is called.

Constraint:
LDA≥max1,N.

5: ANORM – REAL (KIND=nag_wp)Input

On entry: the 1-norm of the original matrix A, which may be computed by calling F06RCF with its parameter NORM='1'. ANORM must be computed either before calling F07FDF (DPOTRF) or else from a copy of the original matrix A.

Constraint:
ANORM≥0.0.

6: RCOND – REAL (KIND=nag_wp)Output

On exit: an estimate of the reciprocal of the condition number of A. RCOND is set to zero if exact singularity is detected or the estimate underflows. If RCOND is less than machine precision, A is singular to working precision.

6 Error Indicators and Warnings

If INFO=-i, the ith parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.

7 Accuracy

The computed estimate RCOND is never less than the true value ρ, and in practice is nearly always less than 10ρ, although examples can be constructed where RCOND is much larger.

8 Further Comments

A call to F07FGF (DPOCON) involves solving a number of systems of linear equations of the form Ax=b; the number is usually 4 or 5 and never more than 11. Each solution involves approximately 2⁢n2 floating point operations but takes considerably longer than a call to F07FEF (DPOTRS) with one right-hand side, because extra care is taken to avoid overflow when A is approximately singular.